Given the equation: xy = 24, how would you up the integral to find the length of the path from x = a to x = b. How would you write the integrand? Thank you!
2007-04-08 08:40:51 · 3 answers · asked by Mrs.Sizemore 2 in Science & Mathematics ➔ Mathematics
s= Int (a_b) sqrt[1+(24/x^2)^2]
( the interval a_b can not include the point x=0)
2007-04-08 08:50:25 · answer #1 · answered by santmann2002 7 · 0⤊ 0⤋
I would rewrite the equation as y = 24/x and then integrate from a to b. The integral of 24/x is -24/x². Substitute b in for x and then substitute a in for x. Subtract the result of the second (a) from the result of the first (b), and you have your answer:
-24/b² - (-24/a²) = 24/a² - 24/b²
2007-04-08 15:50:30 · answer #2 · answered by Dave 6 · 0⤊ 0⤋
I agree with santmann, the element of path length ds is the hypotenuse of a triangle with dx the bottom and dy the side.
ds= sqrt (dx^2 + dy^2)
y = 24/x so dy = -24/x^2 dx
put the integral of ds in terms of dx, from a to b
2007-04-08 16:10:31 · answer #3 · answered by kev1ntx 3 · 0⤊ 0⤋